Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the population mean amount of cola in the bottles filled by Machine 1 is the same as the population mean amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Leah uses the manufacturer's specification to assume that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. She randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let μ1 be the population mean amount of cola in bottles filled by Machine 1 and μ2 be the population mean amount of cola in bottles filled by Machine 2. The p-value is less than 0.001, α=0.05, the null hypothesis is H0:μ1−μ2=0, and the alternative hypothesis is Ha:μ1−μ2≠0. Machine 1 Machine 2 x¯¯¯1=12.524 x¯¯¯2=12.518 n1=244 n2=251 Which of the following statements are accurate for this hypothesis test to evaluate the claim that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount in bottles filled by Machine 2 is not equal to zero? Select all that apply: Reject the null hypothesis that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is equal to zero. Fail to reject the null hypothesis that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is equal to zero. Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to support the claim that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is not equal to zero. Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is not equal to zero.

Name: Leah Peschel is the bottling department manager for a bottling company
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verif

Question

Leah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the population mean amount of cola in the bottles filled by Machine 1 is the same as the population mean amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Leah uses the manufacturer's specification to assume that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. She randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let μ1 be the population mean amount of cola in bottles filled by Machine 1 and μ2 be the population mean amount of cola in bottles filled by Machine 2. The p-value is less than 0.001, α=0.05, the null hypothesis is H0:μ1−μ2=0, and the alternative hypothesis is Ha:μ1−μ2≠0.

Machine 1	Machine 2
x¯¯¯1=12.524	x¯¯¯2=12.518
n1=244	n2=251

Which of the following statements are accurate for this hypothesis test to evaluate the claim that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount in bottles filled by Machine 2 is not equal to zero?

Select all that apply:

Reject the null hypothesis that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is equal to zero.
Fail to reject the null hypothesis that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is equal to zero.
Based on the results of the hypothesis test, there is enough evidence at the α=0.05 level of significance to support the claim that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is not equal to zero.
Based on the results of the hypothesis test, there is not enough evidence at the α=0.05 level of significance to suggest that the true difference between the population mean amount of cola in bottles filled by Machine 1 and the population mean amount of cola in bottles filled by Machine 2 is not equal to zero.